Distributed lag models for retrospective cohort data with application to a study of built environment and body weight

Distributed lag models (DLMs) estimate the health effects of exposure over multiple time lags prior to the outcome and are widely used in time series studies. Applying DLMs to retrospective cohort studies is challenging due to inconsistent lengths of exposure history across participants, which is common when using electronic health record databases. A standard approach is to define subcohorts of individuals with some minimum exposure history, but this limits power and may amplify selection bias. We propose alternative full-cohort methods that use all available data while simultaneously enabling examination of the longest time lag estimable in the cohort. Through simulation studies, we find that restricting to a subcohort can lead to biased estimates of exposure effects due to confounding by correlated exposures at more distant lags. By contrast, full-cohort methods that incorporate multiple imputation of complete exposure histories can avoid this bias to efficiently estimate lagged and cumulative effects. Applying full-cohort DLMs to a study examining the association between residential density (a proxy for walkability) over 12 years and body weight, we find evidence of an immediate effect in the prior 1-2 years. We also observed an association at the maximal lag considered (12 years prior), which we posit reflects an earlier ($\ge$12 years) or incrementally increasing prior effect over time. DLMs can be efficiently incorporated within retrospective cohort studies to identify critical windows of exposure.